We assume that the fluid at a distance \(x\)  is a two-phase fluid. The present model has been termed “ideal momentum” to distinguish it from “ideal energy” and “lossy” models including momentum, energy or mass loss parameters, developed by the present authors and to be reported in detail in a subsequent article. Accordingly, first assume conservation of momentum, i.e. the momentum of the two-phase fluid is solely that from the original input pressure. The droplets transfer momentum to the initially static fluid by drag forces [1]}, [2]} and they reach local dynamic equilibrium in such a way that both phases move at the same speed \(v\)  inside the jet [3]}; this is also the main assumption under the wide class of “Locally Homogeneous Flows” (LHF) [4]}, [5]}, [6]}. We assume that the latter process occurs so fast immediately outside the nozzle's exit that we may neglect the non-equilibrium zone near the nozzle. The latter assumption is reasonable for high-speed pressure atomized jets, e.g. like the ones used in real life diesel engines [7]}. This effectively allows us to treat the two-phase flow as a single fluid with a composite density \(\rho (x)\)  and a single velocity \(v(x)\), depending on the distance from the nozzle, \(x\) .
